Stereoscopic depth perception depends on the slight disparities (position shifts) between the retinal images of the left and right eyes. Knowing how the visual system detects these disparities and uses them to compute depth is not only essential for understanding human recognition of visual objects and perception of three-dimensional visual space, but also important for finding effective treatment for clinical cases of retinal correspondence deficits and for improving machine-vision algorithms for object recognition, robotics, and visual prosthetic devices. In the traditional view, stereopsis finds corresponding features of the retinal images of the two eyes through a one-dimensional (horizontal) matching process and converts the disparities of these features into perceived depth. In this proposal it is demonstrated that such a matching process, and any stereoscopic depth perception dependent on it, would fail in naturalistic visual scenes containing overlapping surfaces. New models are presented which use physiologically realistic neuronal elements to describe stereoscopic correspondence matching as a two-dimensional process. The models are developed and tested in research having four specific experimental aims: (1) to determine how stereoscopic performance depends on stimulus orientation and disparity direction; (2) to identify the stimulus primitives used in human stereoscopic matching; (3) to identify the stimulus and computational requirements of transparency perception; (4) to examine mechanisms of depth constancy operating during torsional rotation of the eyes. To achieve these aims a variety of traditional and novel psychophysical methods will be used. In many of the proposed experiments, these methods will be applied to a new class of visual stimuli: stereo plaids. Sharing characteristics of naturalistic, multi-object visual scenes, stereo plaids allow disparity detection and depth computation to be dissociated for separate experimental examination. The resulting data will reveal stereoscopic processes that have not previously been accessible for separate study.